The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of high school and college students. These same ideas, this development, are available in the following books to any student who is willing to read, to be stimulated, and to learn.

Algebra is an elementary algebra text from one of the leading mathematicians of the world -- a major contribution to the teaching of the very first high school level course in a centuries old topic -- refreshed by the author's inimitable pedagogical style and deep understanding of mathematics and how it is taught and learned.

Author Bio

Gelfand, I.M. : Rutgers the State University of New Jersey Central Office

1. Introduction 2. Exchange of terms in addition 3. Exchange of terms in multiplication 4. Addition in the decimal number system 5. The multiplication table and the multiplication algorithm 6. The division algorithm 7. The binary system 8. The commutative law 9. The associative law 10. The use of parentheses 11. The distributive law 12. Letters in algebra 13. The addition of negative numbers 14. The multiplication of negative numbers 15. Dealing with fractions 16. Powers 17. Big numbers around us 18. Negative powers 19. Small numbers around us 20. How to multiply a m by a n , or why our definition is convenient 21. The rule of multiplication for powers 22. Formula for short multiplication: The square of a sum 23. How to explain the square of the sum formula to your younger brother or sister 24. The difference of squares 25. The cube of the sum formula 26. The formula for (a +b ) 4 27. Formulas for (a +b ) 5 , (a +b ) 6 ,... and Pascal's triangle 28. Polynomials 29. A digression: When are polynomials equal? 30. How many monomials do we get? 31. Coefficients and values 32. Factoring 33. Rational expressions 34. Converting a rational expression into the quotient of two polynomials 35. Polynomials in one variable 36. Division of polynomials in one variable; the remainder 37. The remainder when dividing by x - a 38. Values of polynomials, and interpolation 39. Arithmetic progressions 40. The sum of an arithmetic progression 41. Geometric progressions 42. The sum of a geometric progression 43. Different problems about progressions 44. The well-tempered clavier 45. The sum of an infinite geometric progression 46. Equations 47. A short glossary 48. Quadratic equations 49. The case p = 0. Square roots 50. Rules for square roots 51. The equation x 2 +px + q =0 52. Vieta's theorem 53. Factoring ax 2 +bx +c 54. A formula for ax 2 +bx +c =0(where a does not equal 0) 55. One more formula concerning quadratic equations 56. A quadratic equation becomes linear 57. The graph of the quadratic polynomial 58. Quadratic inequalities 59. Maximum and minimum values of a quadratic polynomial 60. Biquadratic equations 61. Symmetric equations 62. How to confuse students on an exam 63. Roots 64. Non-integer powers 65. Proving inequalities 66. Arithmetic and geometric means 67. The geometric mean does not exceed the arithmetic mean 68. Problems about maximum and minimum 69. Geometric illustrations 70. The arithmetic and geometric means of several numbers 71. The quadratic mean 72. The harmonic mean

The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of high school and college students. These same ideas, this development, are available in the following books to any student who is willing to read, to be stimulated, and to learn.

Algebra is an elementary algebra text from one of the leading mathematicians of the world -- a major contribution to the teaching of the very first high school level course in a centuries old topic -- refreshed by the author's inimitable pedagogical style and deep understanding of mathematics and how it is taught and learned.

Author Bio

Gelfand, I.M. : Rutgers the State University of New Jersey Central Office

1. Introduction 2. Exchange of terms in addition 3. Exchange of terms in multiplication 4. Addition in the decimal number system 5. The multiplication table and the multiplication algorithm 6. The division algorithm 7. The binary system 8. The commutative law 9. The associative law 10. The use of parentheses 11. The distributive law 12. Letters in algebra 13. The addition of negative numbers 14. The multiplication of negative numbers 15. Dealing with fractions 16. Powers 17. Big numbers around us 18. Negative powers 19. Small numbers around us 20. How to multiply a m by a n , or why our definition is convenient 21. The rule of multiplication for powers 22. Formula for short multiplication: The square of a sum 23. How to explain the square of the sum formula to your younger brother or sister 24. The difference of squares 25. The cube of the sum formula 26. The formula for (a +b ) 4 27. Formulas for (a +b ) 5 , (a +b ) 6 ,... and Pascal's triangle 28. Polynomials 29. A digression: When are polynomials equal? 30. How many monomials do we get? 31. Coefficients and values 32. Factoring 33. Rational expressions 34. Converting a rational expression into the quotient of two polynomials 35. Polynomials in one variable 36. Division of polynomials in one variable; the remainder 37. The remainder when dividing by x - a 38. Values of polynomials, and interpolation 39. Arithmetic progressions 40. The sum of an arithmetic progression 41. Geometric progressions 42. The sum of a geometric progression 43. Different problems about progressions 44. The well-tempered clavier 45. The sum of an infinite geometric progression 46. Equations 47. A short glossary 48. Quadratic equations 49. The case p = 0. Square roots 50. Rules for square roots 51. The equation x 2 +px + q =0 52. Vieta's theorem 53. Factoring ax 2 +bx +c 54. A formula for ax 2 +bx +c =0(where a does not equal 0) 55. One more formula concerning quadratic equations 56. A quadratic equation becomes linear 57. The graph of the quadratic polynomial 58. Quadratic inequalities 59. Maximum and minimum values of a quadratic polynomial 60. Biquadratic equations 61. Symmetric equations 62. How to confuse students on an exam 63. Roots 64. Non-integer powers 65. Proving inequalities 66. Arithmetic and geometric means 67. The geometric mean does not exceed the arithmetic mean 68. Problems about maximum and minimum 69. Geometric illustrations 70. The arithmetic and geometric means of several numbers 71. The quadratic mean 72. The harmonic mean